In this paper, we analyze the high-SNR regime of the$M\times K$Network MISO channel in which each transmitter has access to a different channel estimate, possibly with different precision. It has been recently shown that, for some regimes, this setting attains the same Degrees-of-Freedom as the ideal centralized setting with perfect Channel State Information (CSI) sharing, in which all the transmitters are endowed with the best estimate available at any transmitter. This result is restricted by the limitations of the Degrees-of-Freedom metric, as it only provides information about the slope of growth of the capacity as a function of the SNR, without any insight about the possible performance at a given SNR. In order to overcome this limitation, we analyze the affine approximation of the rate on the high-SNR regime for this decentralized Network MISO setting for the antenna configurations in which it achieves the Degrees-of-Freedom of the centralized setting. We show that, for a regime of antenna configurations, it is possible to asymptotically attain the same achievable rate as in the ideal centralized scenario. Consequently, it is possible to achieve the beamforming gain of the ideal perfect-CSI-sharing setting even if only a subset of transmitters is endowed with precise CSI, which can be exploited in scenarios such as distributed massive MIMO where the number of transmit antennas is much bigger than the number of served users. This outcome is a consequence of the synergistic compromise between CSI precision at the transmitters and consistency between the locally-computed precoders, which is an inherent trade-off of decentralized settings that does not exist in the centralized CSI configuration. We propose a precoding scheme achieving the previous result, which is built on an uneven structure in which some transmitters reduce the precision of their own precoding vector for the sake of using transmission parameters that can be more easily predicted by the other transmitters.

This paper studies a memoryless state-dependent multiple access channel (MAC) where two transmitters wish to convey a message to a receiver under the assumption of causal and imperfect channel state information at transmitters (CSIT) and imperfect channel state information at receiver (CSIR). In order to emphasize the limitation of transmitter cooperation between physically distributed nodes, we focus on the so-called distributed CSIT assumption, i.e., where each transmitter has its individual channel knowledge, while the message can be assumed to be partially or entirely shared a priori between transmitters by exploiting some on-board memory. Under this setup, the first part of the paper characterizes the common message capacity of the channel at hand for arbitrary CSIT and CSIR structure. The optimal scheme builds on Shannon strategies, i.e., optimal codes are constructed by letting the channel inputs be a function of current CSIT only. For a special case when CSIT is a deterministic function of CSIR, the considered scheme also achieves the capacity region of a common message and two private messages. The second part addresses an important instance of the previous general result in a context of a cooperative multi-antenna Gaussian channel under i.i.d. fading operating in frequency-division duplex mode, such that CSIT is acquired via an explicit feedback of perfect CSIR. The capacity of the channel at hand is achieved by distributed linear precoding applied to Gaussian codes. Surprisingly, we demonstrate that it is suboptimal to send a number of data streams bounded by the number of transmit antennas as typically considered in a centralized CSIT setup. Finally, numerical examples are provided to evaluate the sum capacity of the binary MAC with binary states as well as the Gaussian MAC with i.i.d. fading.

Unsupervised anomaly detection on time-series is widespread in the industry and an active research topic. Recently, impressive results have been obtained by leveraging the progresses of deep learning, and in particular through the use of Long Short Term Memory (LSTM) neural networks. Yet, latest state-of-the-art unsupervised LSTM-based solutions still require a priori knowledge about normality as they need to train the model on time-series without any anomaly. In contrast, we propose a novel anomaly detector, coined as LSTM-Decomposed (LSTM-D), that does not require this normality knowledge. More specifically, we pre-process the timeseries with a spectral based information reduction such that the LSTM-based detector receiving the time-series becomes less likely to learn the anomaly, and hence miss its detection. We motivate our intuitions through simple examples and verify the performance improvement with respect to state-of-the-art solutions in a reference and publicly available data set.

We address the problem of resource allocation (RA) for spectrum underlay in a cognitive radio (CR) communication system with multiple secondary operators sharing resource with an incumbent primary operator. The multiple secondary operator RA problem is well known to be especially challenging because of the inter-operator coupling constraints arising in the optimization problem, which render impractical inter-operator information exchange necessary. In this paper, we consider a satellite setting for multi-operator CR. In the CR maturation regime, i.e., the period in which the secondary subscriber density is growing yet remains much below that of incumbent users, we show that in fact the inter-operator mutual constraints can be neglected, thus making distributed (across secondary operators) optimization possible. Furthermore, we establish analytically that the mutual constraints asymptotically vanish with the primary user density.

In this work, we study the impact of imperfect sharing of the Channel State Information (CSI) available at the transmitters on a Network MIMO setting in which a set of M transmit antennas, possibly not co-located, jointly serve two multi-antenna users endowed with N1and N2antennas, respectively. We consider the case where only a subset of k transmit antennas have access to perfect CSI, whereas the other M - k transmit antennas have only access to finite precision CSI. The analysis of this configuration aims to answer the question of how much an extra informed antenna can help. We model this scenario as a Decentralized MIMO Broadcast Channel (BC) and characterize the Degrees-of-Freedom (DoF) region, showing that only k = max(N1, N2) antennas with perfect CSI are needed to achieve the DoF of the conventional BC with ubiquitous perfect CSI.

This work identifies the optimal Degrees-ofFreedom (DoF) of the K-User MISO Broadcast Channel (BC) with delayed Channel-State Information at the Transmitter (CSIT) and with additional current noisy CSIT where the current channel estimation error scales in P-αfor α ∈ [0, 1]. These two settings had in the past been studied separately; the setting of imperfect current CSIT has attracted considerable interest over the last decade, while the setting of delayed CSIT was studied in the seminal work of Maddah-Ali and Tse in 2010 1 where an optimal DoF of K/ Σk=1K1/k was established. Since k=1 then there have been several efforts to combine the two settings of delayed and imperfect-current CSIT. Our work establishes for the first time the optimal DoF in this joint setting, capitalizing on a novel transmission scheme that is presented here, which combines a structurally new approach of handling past and current interference, to achieve the optimal performance. We establish the once elusive optimal DoF to be of the form 1 αK + (1 - α)K/(K/ Σk=1K1/k). This further shows that the two k=1 types of DoF gains, from current and delayed CSIT, can be combined additively.

In this work, we consider the sum rate performance of joint processing coordinated multi-point transmission network (JP-CoMP, a.k.a Network MIMO) in a so-called distributed channel state information (D-CSI) setting. In the D-CSI setting, the various transmitters (TXs) acquire a local, TX-dependent, estimate of the global multi-user channel state matrix obtained via terminal feedback and limited backhauling. The CSI noise across TXs can be independent or correlated, so as to reflect the degree to which TXs can exchange information over the backhaul, hence allowing to model a range of situations bridging fully distributed and fully centralized CSI settings. In this context we aim to study the price of CSI distributiveness in terms of sum rate at finite SNR when compared with conventional centralized scenarios. We consider the family of JP-CoMP precoders known as regularized zero-forcing (RZF). We conduct our study in the large scale antenna regime, as it is currently envisioned to be used in real 5G deployments. It is then possible to obtain accurate approximations on so-called deterministic equivalents of the signal to interference and noise ratios. Guided by the obtained deterministic equivalents, we propose an approach to derive a RZF scheme that is robust to the distributed aspect of the CSI, whereby the key idea lies in the optimization of a TX-dependent power level and regularization factor. Our analysis confirms the improved robustness of the proposed scheme with respect to CSI inconsistency at different TXs, even with moderate number of antennas and receivers (RXs).

We study the Degrees-of-Freedom (DoF) in a wireless setting in which K Transmitters (TXs) aim at jointly serving K users. The performance is studied when the TXs are faced with a distributed Channel State Information (CSI) configuration in which each TX has access to its own multi-user imperfect channel estimate based on which it designs its transmit coefficients. The channel estimates are not only imperfectly acquired but they are also imperfectly shared between the TXs. Our first contribution consists of computing a genie-aided upper bound for the DoF of that setting. Our main contribution is then to develop a new robust transmission scheme that leverages the different qualities of CSI available at the TXs to improve the achieved DoF. We show the surprising result that there is a CSI regime, coined the Weak-CSIT regime, in which the genie-aided upper bound is achieved by the proposed transmission scheme. Interestingly, the optimal DoF in the Weak-CSIT regime only depends on the CSI quality at the best informed TX and not on the CSI quality at all other TXs.

Using out-of-band (OOB) side-information has recently been shown to accelerate beam selection in single-user millimeter wave (mmWave) massive MIMO (m-MIMO) communications. In this paper, we propose a novel OOB-aided beam selection framework for a mmWave uplink multi-user system. In particular, we exploit spatial information extracted from lower (sub-6 GHz) bands in order to assist with an inter-user coordination scheme at mmWave bands. Our strategies consider the existence of a low-rate direct device-to-device (D2D) link between suitable pairs of users (UEs), enabling some information exchange. The decentralized coordination mechanism allows the suppression of the so-called co-beam interference which would otherwise lead to irreducible interference at the base station (BS) side, thereby triggering substantial spectral efficiency (SE) gains.

The synergetic gains of spectrum sharing and millimeter wave (mmWave) communication networks have recently attracted attention, owing to the interference canceling benefits of highly-directional beamforming in such systems. In principle, fine-tuned coordinated scheduling and beamforming can drastically reduce cross-operator interference. Unfortunately, this goes at the expense of the exchange of channel state information which is not realistic in particular when considering inter-operator coordination. Indeed, such an exchange of information is expensive in terms of backhaul infrastructure and it raises sensitive privacy issues between otherwise competing operators. In this paper, we expose the existence of a trade-off between coordination and privacy. We propose an algorithm capable of balancing spectrum sharing performance with privacy preservation based on the sharing of a low-rate beam index information where the information is subject to a data obfuscation mechanism borrowed from the digital security literature so as to control the privacy.

In this paper1, we analyze a Network MIMO channel with 2 Transmitters (TXs) jointly serving 2 users, where each TX has a different multi-user Channel State Information (CSI), potentially with a different accuracy. Recently it was shown the surprising result that this decentralized setting can attain the same Degrees-of-Freedom (DoF) as its genie-aided centralized counterpart in which both TXs share the best-quality CSI. However, the DoF derivation alone does not characterize the actual rate and the question was left open as to how big the rate gap between the centralized and the decentralized settings was going to be. In this paper, we considerably strengthen the previous intriguing DoF result by showing that it is possible to achieve asymptotically the same sum rate as that attained by Zero-Forcing (ZF) precoding in a centralized setting endowed with the best-quality CSI. This result involves a novel precoding scheme which is tailored to the decentralized case. The key intuition behind this scheme lies in the striking of an asymptotically optimal compromise between i) realizing high enough precision ZF precoding while ii) maintaining consistent-enough precoding decisions across the non-communicating cooperating TXs.

The availability of accurate and, most importantly, shared channel state information at the transmitter (CSIT) is one of the key factors that enable transmitters cooperation in decentralized wireless systems. However, in some cases, channel information may not be easily or perfectly shared among the transmitters, thus limiting their coordination capabilities. In this paper we shed some light on the fundamental limits of networks with cooperating transmitters impaired by a general distributed CSIT assumption. To this end, we consider a state-dependent memory-less multiple-access channel with common message, and with noisy causal CSIT and noisy channel state information at the receiver (CSIR). Perhaps surprisingly, and in contrast to the same setting in absence of common message, we show that distributed precoding based on current CSIT only (namely, a Shannon strategy) achieves the sum-rate capacity of this channel, for every degree of CSIT and CSIR. By focusing on the transmission of a common message only, we then illustrate this result in a practically relevant Gaussian setting.

Machine learning and data driven approaches have recently received much attention as a key enabler for future 5G and beyond wireless networks. Yet, the evolution towards learning-based data driven networks is still in its infancy, and much of the realization of the promised benefits requires thorough research and development. Fundamental questions remain as to where and how ML can really complement the well-established, well-tested communication systems designed over the last four decades. Moreover, adaptation of machine learning methods is likely needed to realize their full potential in the wireless context. This is particularly challenging for the lower layers of the protocol stack, where the constraints, problem formulation, and even the objectives may fundamentally differ from the typical scenarios to which machine learning has been successfully applied in recent years. In addition, a thorough understanding of the fundamental performance limits is also essential in order to establish quality-of-service guarantees that are common in communication system design. Such challenges, which lie at the core of the special issue, can be categorized into a number of research topics ranging from the optization of neural networks architectures that are suited to wireless communication links (inclusing autoencoders, generative adversarial networks, reinforcement based networks etc) to performance analysis, to the acceleration of data-driven training, and possibly in distributed settings. The application domains within the wireless realm are also quite diverse in nature with promising preliminary results in the area of physical layer design and resource allocation as well as for network service orchestrations. Testbeds and experimental evaluations are also begining to be reported.

Machine learning and data driven approaches have recently received much attention as a key enabler for future 5G and beyond wireless networks. Yet, the evolution towards learning-based data driven networks is still in its infancy, and much of the realization of the promised benefits requires thorough research and development. Fundamental questions remain as to where and how ML can really complement the well-established, well-tested communication systems designed over the last four decades. Moreover, adaptation of machine learning methods is likely needed to realize their full potential in the wireless context. This is particularly challenging for the lower layers of the protocol stack, where the constraints, problem formulation, and even the objectives may fundamentally differ from the typical scenarios to which machine learning has been successfully applied in recent years. In addition, a thorough understanding of the fundamental performance limits is also essential in order to establish quality-of-service guarantees that are common in communication system design. Such challenges, which lie at the core of the special issue, can be categorized into a number of research topics ranging from the optization of neural networks architectures that are suited to wireless communication links (inclusing autoencoders, generative adversarial networks, reinforcement based networks etc) to performance analysis, to the acceleration of data-driven training, and possibly in distributed settings. The application domains within the wireless realm are also quite diverse in nature with promising preliminary results in the area of physical layer design and resource allocation as well as for network service orchestrations. Testbeds and experimental evaluations are also begining to be reported.

Thanks to the recent advances in processing speed, data acquisition and storage, machine learning (ML) is penetrating every facet of our lives, and transforming research in many areas in a fundamental manner. Wireless communications is another success story - ubiquitous in our lives, from handheld devices to wearables, smart homes, and automobiles. While recent years have seen a flurry of research activity in exploiting ML tools for various wireless communication problems, the impact of these techniques in practical communication systems and standards is yet to be seen. In this paper, we review some of the major promises and challenges of ML in wireless communication systems, focusing mainly on the physical layer. We present some of the most striking recent accomplishments that ML techniques have achieved with respect to classical approaches, and point to promising research directions where ML is likely to make the biggest impact in the near future. We also highlight the complementary problem of designing physical layer techniques to enable distributed ML at the wireless network edge, which further emphasizes the need to understand and connect ML with fundamental concepts in wireless communications.

Location-aided beam alignment has been proposed recently as a potential approach for fast link establishment in millimeter wave (mmWave) massive MIMO (mMIMO) communications. However, due to mobility and other imperfections in the estimation process, the spatial information obtained at the base station (BS) and the user (UE) is likely to be noisy, degrading beam alignment performance. In this paper, we introduce a robust beam alignment framework in order to exhibit resilience with respect to this problem. We first recast beam alignment as a decentralized coordination problem where BS and UE seek coordination on the basis of correlated yet individual position information. We formulate the optimum beam alignment solution as the solution of a Bayesian team decision problem. We then propose a suite of algorithms to approach optimality with reduced complexity. The effectiveness of the robust beam alignment procedure, compared with classical designs, is then verified on simulation settings with varying location information accuracies.

This work1analyzes the Generalized Degrees-of-Freedom (GDoF) of the 2-User Multiple-Input Single-Output (MISO) Broadcast Channel (BC) in the so-called Distributed CSIT regime, with application to decentralized wireless networks. This regime differs from the classical limited CSIT one in that the CSIT is not just noisy but also imperfectly shared across the transmitters (TXs). Hence, each TX precodes data on the basis of local CSIT and statistical quality information at other TXs. We derive the GDoF result and obtain the surprising outcome that by specific accounting of the pathloss information, it becomes possible for the decentralized precoded network to reach the same performance as a genie-aided centralized network where the central node has obtained the estimates of both TXs. The key idea allowing this surprising robustness is to let the TXs have asymmetrical roles such that the most informed TX is able to balance the lower CSIT quality at the other TX.

In this paper1we consider the Network MIMO channel under the so-called Distributed Channel State Information at the Transmitters (D-CSIT) configuration. In this setting, the precoder is designed in a distributed manner at each Transmitter (TX) on the basis of local versions of Channel State information (CSI) of various quality. Although the use of simple Zero-Forcing (ZF) was recently shown to reach the optimal DoF for a Broadcast Channel (BC) under noisy, yet centralized, CSI at the TX (CSIT), it can turn very inefficient when faced with D-CSIT: The number of Degrees-of-Freedom (DoF) achieved is then limited by the worst CSI accuracy across TXs. To circumvent this effect, we develop a new robust transmission scheme improving the DoF. A surprising result is uncovered by which, in the regime of so-called weak CSIT, the proposed scheme is shown to be DoF-optimal and to achieve a centralized outerbound consisting in the DoF of a genie-aided centralized setting in which the CSIT versions of all TXs are available everywhere. Building upon the insight obtained in the weak CSIT regime, we develop a general D-CSIT robust scheme for the 3-user case which improves over the DoF obtained by conventional robust approaches for any arbitrary CSIT configuration.

This work1derives the optimal Degrees-of-Freedom (DoF) of the K-User MISO Broadcast Channel (BC) with delayed Channel-State Information at the Transmitter (CSIT) and with additional current noisy CSIT where the channel estimation error scales in P-αfor α ∈ [0, 1]. The optimal sum DoF takes the simple form (1 - α)K/HK+ αK where HK =△ Σk=1K1/k. This optimal performance is the result of a novel scheme which deviates from existing efforts as it digitally combines interference, decodes symbols of any order in the MAT alignment [1], and utilizes a hierarchical quantizer whose output is distributed across rounds in a way that minimizes unwanted interference. These jointly deliver, for the first time, the elusive DoF-optimal combining of MAT and ZF.

In this paper, the operation of a licensed shared access system is investigated, considering downlink communication. The system comprises a multiple-input-single-output (MISO) incumbent transmitter (TX)-receiver (RX) pair, which offers a spectrum sharing opportunity to a MISO licensee TX-RX pair. Our main contribution is the design of a coordinated transmission scheme, inspired by the underlay cognitive radio (CR) approach, with the aim of maximizing the average rate of the licensee, subject to an average rate constraint for the incumbent. In contrast to most prior works on the underlay CR, the coordination of the two TXs takes place under a realistic channel state information (CSI) scenario, where each TX has solely access to the instantaneous direct channel of its served terminal. Such a CSI knowledge setting brings about a formulation based on the theory of Team Decisions, whereby the TXs aim at optimizing a common objective given the same constraint set, on the basis of individual channel information. Consequently, a novel set of applicable precoding schemes consisting in letting the two TXs cooperate on the basis of the statistical information is proposed. We verify by simulations that this novel, practically relevant, coordinated precoding scheme outperforms the standard underlay CR approach.

International audience

Obtaining accurate Channel State Information (CSI) at multiple Transmitters (TXs) is critical to the performance of many cooperative transmission schemes, including joint precoding in the context of network MIMO. Practical CSI feedback and limited backhaul-based sharing creates degradations of CSI which are specific to each TX, giving rise to a Distributed (D-) CSI configuration. In the D-CSI broadcast channel setting, each TX implements separate elements of the joint multi-user precoder based on its own individual CSI estimate. In this work, we presents a first finite-SNR regime rate analysis for a network-MIMO (broadcast channel) under a distributed CSI setting. Of particular importance is the notion of a “price of distributedness” which penalizes the D-CSI setting over the conventional centralized one with the same overall feedback quality. To tackle this problem, we apply tools from the field of Random Matrix Theory (RMT) to derive deterministic equivalents of the Signal to Interference plus Noise Ratio (SINR) for a popular class of precoders. Our key finding lies in the notion that the price of distributedness converges to a predictable value, bounded away from zero, as the number of antennas grows.1

In this paper, we study the problem of the optimal dissemination of channel state information (CSI) among K spatially distributed transmitters (TXs) jointly cooperating to serve K receivers. One of the particularities of this paper lies in the fact that the CSI is distributed in the sense that each TX obtains its own estimate of the global multiuser MIMO channel with no further exchange of information being allowed between the TXs. Although this is well suited to model the cooperation between noncolocated TXs, e.g., in cellular coordinated multipoint schemes, this type of setting has received little attention so far in the information theoretic society. We study in this paper what are the CSI requirements at every TX, as a function of the network geometry, to ensure that the maximal number of degrees-of-freedom (DoF) is achieved, i.e., the same DoF as obtained under perfect CSI at all TXs. We advocate the use of the generalized DoF to take into account the geometry of the network in the analysis. Consistent with the intuition, the derived generalized DoF maximizing CSI allocation policy suggests that TX cooperation should be limited to a specific finite neighborhood around each TX. This is in sharp contrast with the conventional (uniform) CSI dissemination policy, which induces CSI requirements that grow unbounded with the network size. The proposed CSI allocation policy suggests an alternative to clustering, which overcomes fundamental limitations, such as: 1) edge interference and 2) unbounded increase of the CSIT requirements with the cluster size. Finally, we show how finite neighborhood CSIT exchange translates into finite neighborhood message exchange so that finally global interference management is possible at finite SNR with only local cooperation.

In this work we study the impact of having only incomplete channel state information at the transmitters (CSIT) over the feasibility of interference alignment (IA) in a K-user MIMO interference channel (IC). Incompleteness of CSIT refers to the perfect knowledge at each transmitter (TX) of only a sub-matrix of the global channel matrix, where the sub-matrix is specific to each TX. This paper investigates the notion of IA feasibility for CSIT configurations being as incomplete as possible, as this leads to feedback overhead reductions in practice. We distinguish between antenna configurations where (i) removing a single antenna makes IA unfeasible, referred to as tightly-feasible settings, and (ii) cases where extra antennas are available, referred to as super-feasible settings. We show conditions for which IA is feasible in strictly incomplete CSIT scenarios, even in tightly-feasible settings. For such cases, we provide a CSIT allocation policy preserving IA feasibility while reducing significantly the amount of CSIT required. For super-feasible settings, we develop a heuristic CSIT allocation algorithm which exploits the additional antennas to further reduce the size of the CSIT allocation. As a byproduct of our approach, a simple and intuitive algorithm for testing feasibility of single stream IA is provided.

We consider the problem of downlink precoding for Network (multi-cell) MIMO networks where Transmitters (TXs) are provided with imperfect Channel State Information (CSI). Specifically, each TX receives a delayed channel estimate with the delay being specific to each channel component. This model is particularly adapted to the scenarios where a user feeds back its CSI to its serving base only as it is envisioned in future LTE networks. We analyze the impact of the delay during the backhaul-based CSI exchange on the rate performance achieved by Network MIMO. We highlight how delay can dramatically degrade system performance if existing precoding methods are to be used. We propose an alternative robust beamforming strategy which achieves the maximal performance, in DoF sense. We verify by simulations that the theoretical DoF improvement translates into a performance increase at finite Signal-to-Noise Ratio (SNR) as well1.

The degrees of freedom (DoF) of a K-User MISO broadcast channel (BC) is studied when the transmitter (TX) has access to a delayed channel estimate in addition to an imperfect estimate of the current channel. The current estimate could be for example obtained from prediction applied on past estimates, in the case where feedback delay is within the coherence time. Prior results in this setting are promising, yet remain limited to the two-user case. In contrast, we consider here an arbitrary number of users. We develop a new transmission scheme, called the Kα-MAT scheme, which builds upon both the principle of the MAT alignment from Maddah-Ali and Tse and zero-forcing (ZF) to achieve a larger DoF in the channel state information (CSI) configuration previously described. We also develop a new upper bound for the DoF to compare with the DoF achieved by Kα-MAT. Although not optimal, the Kα-MAT scheme performs well when the CSIT quality is not too delayed or K is small. The Kα-MAT scheme can be seen as a robust version of ZF with respect to the delay in the CSI feedback.

In this work1, we consider the joint precoding across K transmitters (TXs), sharing the knowledge of the user's data symbols being transmitted to K single-antenna receivers (RXs). We consider a distributed channel state information (DCSI) configuration where each TX has its own local estimate of the overall multiuser MIMO channel. Our focus is on the optimization of the allocation of the CSI feedback subject to a constraint on the total amount of feedback. As a starting point, we consider the Wyner model where we derive a distance-based CSI allocation achieving close to the optimal performance using only a small percentage of the total feedback. The approach relies on the exploitation of the attenuation to restrict the cooperation at a local scale. Indeed, the CSI and the user's data symbols are then shared to only a finite number of neighbors such that our approach appears as an improved alternative to clustering.

In this work, we consider the joint precoding across K distant transmitters (TXs) towards K single-antenna receivers (RXs) and we let the TXs have access to perfect Channel State Information (CSI). Instead of considering the conventional method of clustering to allocate the user's data symbols, we focus on determining the most efficient symbol sharing patterns. Consequently, we optimize directly the user's data symbol allocation subject to a constraint on the total number of user's data bits transmitted through the core network. We develop a novel approach whereby sparse precoders approximating the true precoders are computed. These precoders require only a fraction of the overall symbol sharing overhead while introducing only limited losses. Thereby, allocating the symbols only to their nonzero coefficients leads to very efficient symbol sharing (or routing) algorithms. Furthermore, these algorithms have a much lower complexity that conventional approaches. By simulations, we show that our approach outperforms clustering-based multicell MIMO methods from the literature and that the routing obtained is mainly dependent on the pathloss structure and can be applied using only long term CSI with reduced losses.

In this paper, we discuss the joint precoding with finite rate feedback in the so-called network multiple-input multiple-output (MIMO) where the TXs share the knowledge of the data symbols to be transmitted. We introduce a distributed channel state information (DCSI) model where each TX has its own local estimate of the overall multiuser MIMO channel and must make a precoding decision solely based on the available local CSI. We refer to this channel as the DCSI-MIMO channel and the precoding problem as distributed precoding. We extend to the DCSI setting the work from Jindal in 2006 for the conventional MIMO broadcast channel (BC) in which the number of degrees of freedom (DoFs) achieved by zero forcing (ZF) was derived as a function of the scaling in the logarithm of the signal-to-noise ratio of the number of quantizing bits. Particularly, we show the seemingly pessimistic result that the number of DoFs at each user is limited by the worst CSI across all users and across all TXs. This is in contrast to the conventional MIMO BC where the number of DoFs at one user is solely dependent on the quality of the estimation of his own feedback. Consequently, we provide precoding schemes improving on the achieved number of DoFs. For the two-user case, the derived novel precoder achieves a number of DoFs limited by the best CSI accuracy across the TXs instead of the worst with conventional ZF. We also advocate the use of hierarchical quantization of the CSI, for which we show that considerable gains are possible. Finally, we use the previous analysis to derive the DoFs optimal allocation of the feedback bits to the various TXs under a constraint on the size of the aggregate feedback in the network, in the case where conventional ZF is used.

In this paper, the rate region of the two user MIMO broadcast channel (BC) under linear filtering at high signal-to-noise ratio (SNR) is investigated when time sharing is not available and the transmitter has more antennas than the sum of the receiving antennas. To reach the rate region's boundary, the sum rate is maximized subject to a given ratio between the users rates. The sum rate is first considered asymptotically when the SNR tends to infinity and taken as an affine function of the logarithm of the SNR, with the multiplicative and the additive parameters called the multiplexing gain (MG) and the rate offset (RO), respectively. The maximal MG and the maximal RO are obtained for every rate ratio constraint. Additionally, the asymptotic optimal stream allocations that achieve those values are also derived. Analytical inner and outer bounds, which offer a rough approximation of the boundary but are extremely easy to evaluate even in fading channels, are then developed. The maximization of the rate subject to a rate ratio constraint is then studied at finite SNR. Algorithmic inner and outer bounds for the rate region boundary are derived and shown to be very close to each other and accurate even at intermediate SNR.

In this work1, the joint precoding across two distant transmitters (TXs), sharing the knowledge of the data symbols to be transmitted, to two receivers (RXs), each equipped with one antenna, is discussed. We consider a distributed channel state information (CSI) configuration where each TX has its own local estimate of the channel and no communication is possible between the TXs. Based on the distributed CSI configuration, we introduce a concept of distributed MIMO precoding. We focus on the high signal-to-noise ratio (SNR) regime such that the two TXs aim at designing a precoding matrix to cancel the interference. Building on the study of the multiple antenna broadcast channel, we obtain the following key results: We derive the multiplexing gain (MG) as a function of the scaling in the SNR of the number of bits quantizing at each TX the channel to a given RX. Particularly, we show that the conventional Zero Forcing precoder is not MG maximizing, and we provide a precoding scheme optimal in terms of MG. Beyond the established MG optimality, simulations show that the proposed precoding schemes achieve better performances at intermediate SNR than known linear precoders.

In this paper, we present a general analytical framework for the exact mutual information (MI) cumulants of multiple-input multiple-output (MIMO) systems with perfect receiver channel state information (CSI) and no transmitter CSI. Our derivation is based on a recent parameterization of the joint ordered eigenvalue probability density function (PDF), that encompasses both uncorrelated/semi-correlated Rayleigh channels as well as uncorrelated Rician channels. In addition, we extend our framework to account for the cumulants of doubly-correlated Rayleigh channels and also to deduce tractable expressions in the high Signal-to-Noise ratio (SNR) regime. The cumulants are particularly useful to study all high-order statistics (HOS) of the MI; in fact, they can be used to express the MI mean and variance as a finite sum of determinants. Our analytical expressions are then validated via Monte-Carlo simulations with the attained accuracy being excellent in all cases.

We investigate the maximization of a quotient of two determinants with different exponents under a Frobenius norm constraint, where each determinant is taken from a matrix-valued Hermitian form. The optimum matrix that constitutes the Hermitian forms is shown to be a scaled partial isometry. For the special case of vector-valued Hermitian forms, the optimality condition turns out to be an implicit eigenproblem and we derive an iterative algorithm where in each step the principal eigenvector of a matrix has to be chosen. In addition, we prove monotonic convergence of the iterative algorithm, which means that the utility increases in every step.

In this paper, the rate region of the two user MIMO broadcast channel (BC) with linear filtering at high signal-to-noise ratio (SNR) is studied when time sharing is not available and the transmitter has fewer antennas than the sum of the receiving antennas. To reach the boundary of the rate region, the sum rate is maximized subject to a rate ratio constraint. Furthermore, the sum rate is approximated as an affine function of the logarithm of the SNR and the two parameters of this approximation, which are the multiplexing gain (MG) and the rate offset (RO), are derived. This leads directly to the asymptotic rate region, particularly interesting because it is obtained in simple analytical form and offers a good approximation at high but finite SNR. We then consider the rate region boundary at finite SNR and derive algorithmic bounds for it, which are accurate even at intermediate SNR.

This paper provides a systematic mutual information (MI) and multichannel beamforming (MBF) characterization of optimized multiple-input multiple-output (MIMO) communication systems operating in Ricean fading. These optimized configurations are of high practical importance since, contrary to the common belief, benefit from the presence of direct Line-of-Sight (LoS) components and deliver maximum multiplexing gains, by deploying specifically designed antenna arrays at both ends. In the following, using elements from random matrix theory, novel analytical expressions are derived for the exact and asymptotic MI statistics while the prevalent Gaussian approximation is examined. Moreover, new explicit expressions for the marginal eigenvalues are deduced which are thereafter used to analyze the BF performance of the associated eigenmodes in terms of Signal-to-Noise ratio (SNR) outage probability. We note that all derived formulas are given in tractable determinant form and therefore allow for fast and efficient computation and also yield an excellent match with Monte-Carlo simulations, under different fading scenarios and model parameters.